Remember: in our work flow, we give our images a touch of sharpening after interpolating. Most of these methods work by averaging pixels in some way. This averaging is what's at the heart of the softness that's created, and the reason why we sharpen.
This one is the simplest of them all. This method matches a pixel from the original image to the corresponding position in the resized document. The original colour and tone values are retained and no new averaged colours are created. If no pixel from the original matches the new position, then it duplicates a sample by copying a pixel next to it (thus, it's nearest neighbour). For our purposes, not the tool of choice. This one can be helpful in 1bpc or indexed-colour images.
This one duplicates a sample by averaging the pixels (4) on either side of it. It's faster than the bicubic options, but may not look as good. It is important to note that averaging = the introduction of new colours; new colours which weren't necessarily present in the original.
With this method the image is divided into squares of 4 pixels x 4 pixels, the colour information within each 16 pixel group is used to more accurately predict the appearance of the new resampled pixels. This method is slower than Nearest Neighbor of Bilinear and works fairly well with photographs.
This relatively new version of Bicubic works better for enlarging an image (which is what we are looking for here) and handles post-interpolation sharpening better than Bicubic sampling.
Another new version of Bicubic that works well for downsampling or reducing an image. This one does a better job at preserving detail when downsampling than Bicubic.
There is obviously a ton more to talk about with this. You can get deeper into the math behind these methods if you choose. But for now, this should help you understand the choices presented when you attempt to resize your image from within Photoshop.
In the next installment, we'll look at Interactive Interpolation; which is part of Optipix 3.1 from Reindeer Graphics.